Question: Simplify the following expression: $\sqrt{12}+\sqrt{27}+\sqrt{3}$
First, try to factor any perfect squares out of the radicals. $= \sqrt{12}+\sqrt{27}+\sqrt{3}$ $= \sqrt{4 \cdot 3}+\sqrt{9 \cdot 3}+\sqrt{3}$ Separate the radicals and simplify. $= \sqrt{4} \cdot \sqrt{3}+\sqrt{9} \cdot \sqrt{3}+\sqrt{3}$ $= 2\sqrt{3}+3\sqrt{3}+\sqrt{3}$ Finally, simplify by combining the terms. $= ( 2 + 3 + 1 )\sqrt{3} = 6\sqrt{3}$